Problem: Simplify the following expression: $\dfrac{45z^5}{20z^3}$ You can assume $z \neq 0$.
$ \dfrac{45z^5}{20z^3} = \dfrac{45}{20} \cdot \dfrac{z^5}{z^3} $ To simplify $\frac{45}{20}$ , find the greatest common factor (GCD) of $45$ and $20$ $45 = 3 \cdot 3 \cdot 5$ $20 = 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(45, 20) = 5 $ $ \dfrac{45}{20} \cdot \dfrac{z^5}{z^3} = \dfrac{5 \cdot 9}{5 \cdot 4} \cdot \dfrac{z^5}{z^3} $ $\phantom{ \dfrac{45}{20} \cdot \dfrac{5}{3}} = \dfrac{9}{4} \cdot \dfrac{z^5}{z^3} $ $ \dfrac{z^5}{z^3} = \dfrac{z \cdot z \cdot z \cdot z \cdot z}{z \cdot z \cdot z} = z^2 $ $ \dfrac{9}{4} \cdot z^2 = \dfrac{9z^2}{4} $